Topics
Number System (Including Estimation and Approximation)
Number System
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Ratio and Proportion
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Estimation
Theme 3 : Algebra
Numbers in India and International System (With Comparison)
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Place Value
Negative Numbers and Integers
Geometry
Theme 4 : Geometry
Mensuration
Theme 5 : Mensuration
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Theme 6 : Statistics
Data Handling
Fractions
Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Sets
Percent (Percentage)
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Fundamental Concepts (Including Angles and their Properties)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Triangles (Including Types and Properties of Triangles)
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Recognition of Solids
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Data Handling (Including Mean and Median)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Reading and Writing Large Numbers Using the Hindu-Arabic System
- Examples
- Real-Life Application
- Tips, Tricks, and Common Mistakes
Introduction
Whenever you see a six-digit cheque amount, read India’s population, or hear about a winning lottery, you’re seeing the Hindu-Arabic (Indian) System in action. It helps us make sense of large numbers in daily life!
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10 Digit: Uses symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
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Base-10 System: Each place’s value increases tenfold as you move left.
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Place Value: The value of each digit depends on its position (ones, tens, hundreds, etc.).
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Zero as Placeholder: Allows for representation of any number, large or small.
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Origin: Developed in India and spread by Arab scholars.

Reading and Writing Large Numbers Using the Hindu-Arabic System
In the Indian System, also called the Hindu-Arabic System, to read and write large quantities with ease, the groups are made with certain periods, as shown below:
| Value | 10,00,00,000 | 1,00,00,000 | 10,00,000 | 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
| Period | Ten crore (TC) | Crore (C) |
Ten Lakhs (T L) |
Lakh (L) |
Ten Thousand (T Th) |
Thousand (Th) |
Hundreds (H) |
Tens (T) |
Ones (O) |
Reading and Writing Large Numbers Using the Hindu-Arabic System:
| Periods → |
Crores | Lakhs | Thousands | Ones | |||||
| ↓ Numbers | (TC) | (C) | (TL) |
L |
(TTh) | (Th) | (H) | (T) | (O) |
| 7456123 | 7 | 4 | 5 | 6 | 1 | 2 | 3 | ||
| 225437 |
|
|
2 | 2 | 5 | 4 | 3 | 7 | |
| 61786425 |
|
6 |
1 | 7 | 8 | 6 | 4 | 2 | 5 |
| 82854137 |
|
8 |
2 | 8 | 5 | 4 | 1 | 3 | 7 |
| 743813256 | 7 | 4 | 3 | 8 | 1 | 3 | 2 | 5 | 6 |
Examples
- 7456123 = 74,56,123
= Seventy-four lakh fifty-six thousand one hundred twenty-three. - 82854137 = 8,28,54,137
= Eight crore twenty-eight lakh fifty-four thousand one hundred thirty-seven. - 61786425 = 6,17,86,425
= Six crore seventeen lakh eighty-six thousand four hundred twenty-five. - 82854137 = 8,28,54, 137
= Eight crore twenty-eight lakh fifty-four thousand one hundred thirty-seven. - 743813256 = 74,38,13,256
= Seventy-four crore thirty-eight lakh thirteen thousand two hundred fifty-six.
Note:
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Don’t use plurals when writing numbers in words (e.g., write five thousand, not five thousands).
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Don’t use “and” between tens and ones in number words (e.g., write five hundred ninety-three, not five hundred and ninety-three).
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Don’t use commas when writing numerals like 2,468. Instead, write Two thousand four hundred sixty-eight.
Real-Life Application
1. A check for ₹23,45,678 is written as
- 23,45,678 (figures)
- Twenty-three lakh forty-five thousand six hundred seventy-eight (in words)
2. Population data: “1,38,00,00,000” is spoken as “one hundred thirty-eight crore.”
Tips, Tricks, and Common Mistakes
- Commas: Always write from the right: first three digits, then every two digits.
- No “and” in words. Don’t use “and” (e.g., NOT “two hundred and fifty”).
- No plurals: Use “lakh”, not “lakhs.”
- Commas only in figures, not in words.
- Zero is never at the start (e.g., “07,21,096” is just “7,21,096”).
